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Theorem reli 5171
 Description: The identity relation is a relation. Part of Exercise 4.12(p) of [Mendelson] p. 235. (Contributed by NM, 26-Apr-1998.) (Revised by Mario Carneiro, 21-Dec-2013.)
Assertion
Ref Expression
reli Rel I

Proof of Theorem reli
Dummy variables 𝑥 𝑦 are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 dfid3 4954 . 2 I = {⟨𝑥, 𝑦⟩ ∣ 𝑥 = 𝑦}
21relopabi 5167 1 Rel I
 Colors of variables: wff setvar class Syntax hints:   I cid 4948  Rel wrel 5043 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590 This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-3an 1033  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-rab 2905  df-v 3175  df-dif 3543  df-un 3545  df-in 3547  df-ss 3554  df-nul 3875  df-if 4037  df-sn 4126  df-pr 4128  df-op 4132  df-opab 4644  df-id 4953  df-xp 5044  df-rel 5045 This theorem is referenced by:  ideqg  5195  issetid  5198  iss  5367  intirr  5433  funi  5834  f1ovi  6087  idssen  7886  idsset  31167  bj-elid  32262
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